1) Calcium 40
2) 60 proton, 82 neutrons
Step-by-step explanation:
1)
The graph in the figure represents the stability of nuclei by showing the number of neutrons in the nucleus (y-axis) versus the number of protons in the nucleus (x-axis).
The graph shows that for low number of protons, nuclei are more stable if they contain approximately the same number of protons and neutrons:
[tex]n\sim p[/tex]
However, as the number of protons increases, nuclei becomes more stable if they contain more neutrons than protons, so we see that the band stability is when
[tex]n>p[/tex]
Among the 4 options given in this problem, we observe that the isotop:
Calcium-40
Has 20 protons (atomic number 20) and therefore 20 neutrons. Since it is a nucleus with low number of protons, and its ratio neutrons/protons is close to 1, it means that this is a stable isotope.
2)
In order to check which of these isotopes is stable (not radioactive), we have to see which one of them is along the band of stability.
Let's analyze each of them:
60 protons, 64 neutrons --> not stable: this is an isotope with high number of protons, so the ratio neutrons/protons should be much higher than 1
60 proton, 82 neutrons, --> stable: in this case, we see that the number of neutrons is higher than the number of protons, and by looking at the x-axis at the value p = 60, we see that the point corresponding to n = 82 falls within the band of stability.
60 protons, 90 neutrons --> not stable: in this case, we see that the point falls above the band of stability, because there are too many neutrons
60 protons, 100 neutrons --> not stable: as before, there are too many neutrons
